Question

Find the sum of the finite arithmetic sequence 6, 14, 22, 30, …, 62.

Answer 1

The first term of this sequence is 6 and the common difference is 14 – 6 = 8. We are summing 62 – 6 = 56 equally spaced terms. The sum is halfway between 6 + 8 and 62 – 8, i.e., $56 \cdot \frac12(6 + 62) = \boxed{1820}$.